3,339 research outputs found
Level 2.5 large deviations for continuous time Markov chains with time periodic rates
We consider an irreducible continuous time Markov chain on a finite state
space and with time periodic jump rates and prove the joint large deviation
principle for the empirical measure and flow and the joint large deviation
principle for the empirical measure and current. By contraction we get the
large deviation principle of three types of entropy production flow. We derive
some Gallavotti-Cohen duality relations and discuss some applications.Comment: 37 pages. corrected versio
Perturbative analysis of disordered Ising models close to criticality
We consider a two-dimensional Ising model with random i.i.d. nearest-neighbor
ferromagnetic couplings and no external magnetic field. We show that, if the
probability of supercritical couplings is small enough, the system admits a
convergent cluster expansion with probability one. The associated polymers are
defined on a sequence of increasing scales; in particular the convergence of
the above expansion implies the infinite differentiability of the free energy
but not its analyticity. The basic tools in the proof are a general theory of
graded cluster expansions and a stochastic domination of the disorder
Long range correlations and phase transition in non-equilibrium diffusive systems
We obtain explicit expressions for the long range correlations in the ABC
model and in diffusive models conditioned to produce an atypical current of
particles.In both cases, the two-point correlation functions allow to detect
the occurrence of a phase transition as they become singular when the system
approaches the transition
A nonequilibrium extension of the Clausius heat theorem
We generalize the Clausius (in)equality to overdamped mesoscopic and
macroscopic diffusions in the presence of nonconservative forces. In contrast
to previous frameworks, we use a decomposition scheme for heat which is based
on an exact variant of the Minimum Entropy Production Principle as obtained
from dynamical fluctuation theory. This new extended heat theorem holds true
for arbitrary driving and does not require assumptions of local or close to
equilibrium. The argument remains exactly intact for diffusing fields where the
fields correspond to macroscopic profiles of interacting particles under
hydrodynamic fluctuations. We also show that the change of Shannon entropy is
related to the antisymmetric part under a modified time-reversal of the
time-integrated entropy flux.Comment: 23 pages; v2: manuscript significantly extende
A diffusive system driven by a battery or by a smoothly varying field
We consider the steady state of a one dimensional diffusive system, such as
the symmetric simple exclusion process (SSEP) on a ring, driven by a battery at
the origin or by a smoothly varying field along the ring. The battery appears
as the limiting case of a smoothly varying field, when the field becomes a
delta function at the origin. We find that in the scaling limit, the long range
pair correlation functions of the system driven by a battery turn out to be
very different from the ones known in the steady state of the SSEP maintained
out of equilibrium by contact with two reservoirs, even when the steady state
density profiles are identical in both models
The Pomeron and Odderon in elastic, inelastic and total cross sections at the LHC
A simple model for elastic diffractive hadron scattering, reproducing the
dip-bump structure is used to analyze PP and scattering. The main
emphasis is on the delicate and non-trivial dynamics in the dip-bump region,
near t=-1 GeV. The simplicity of the model and the expected smallness of
the absorption corrections enables one the control of various contributions to
the scattering amplitude, in particular the interplay between the C-even and
C-odd components of the amplitude, as well as their relative contribution,
changing with s and t. The role of the non-linearity of the Regge trajectories
is scrutinized. The ratio of the real to imaginary parts of the forward
amplitude, the ratio of elastic to total cross sections and the inelastic cross
section are calculated. Predictions for the LHC energy region, where most of
the exiting models will be either confirmed or ruled out, are presented.Comment: 16 pages, 13 figures. Small correction. To be published in the
International Journal of Modern Physics
Exact Free Energy Functional for a Driven Diffusive Open Stationary Nonequilibrium System
We obtain the exact probability of finding a
macroscopic density profile in the stationary nonequilibrium state of
an open driven diffusive system, when the size of the system .
, which plays the role of a nonequilibrium free energy, has a very
different structure from that found in the purely diffusive case. As there,
is nonlocal, but the shocks and dynamic phase transitions of the
driven system are reflected in non-convexity of , in discontinuities in
its second derivatives, and in non-Gaussian fluctuations in the steady state.Comment: LaTeX2e, RevTeX4, PiCTeX. Four pages, one PiCTeX figure included in
TeX source fil
Onsager-Machlup theory and work fluctuation theorem for a harmonically driven Brownian particle
We extend Tooru-Cohen analysis for nonequilirium steady state(NSS) of a
Brownian particle to nonequilibrium oscillatory state (NOS) of Brownian
particle by considering time dependent external drive protocol. We consider an
unbounded charged Brownian particle in the presence of an oscillating electric
field and prove work fluctuation theorem, which is valid for any initial
distribution and at all times. For harmonically bounded and constantly dragged
Brownian particle considered by Tooru and Cohen, work fluctuation theorem is
valid for any initial condition(also NSS), but only in large time limit. We use
Onsager-Machlup Lagrangian with a constraint to obtain frequency dependent work
distribution function, and describe entropy production rate and properties of
dissipation functions for the present system using Onsager-Machlup functional.Comment: 6 pages, 1 figur
Hydrodynamic limit for a boundary driven stochastic lattice gas model with many conserved quantities
We prove the hydrodynamic limit for a particle system in which particles may
have different velocities. We assume that we have two infinite reservoirs of
particles at the boundary: this is the so-called boundary driven process. The
dynamics we considered consists of a weakly asymmetric simple exclusion process
with collision among particles having different velocities
Entropy and Nonlinear Nonequilibrium Thermodynamic Relation for Heat Conducting Steady States
Among various possible routes to extend entropy and thermodynamics to
nonequilibrium steady states (NESS), we take the one which is guided by
operational thermodynamics and the Clausius relation. In our previous study, we
derived the extended Clausius relation for NESS, where the heat in the original
relation is replaced by its "renormalized" counterpart called the excess heat,
and the Gibbs-Shannon expression for the entropy by a new symmetrized
Gibbs-Shannon-like expression. Here we concentrate on Markov processes
describing heat conducting systems, and develop a new method for deriving
thermodynamic relations. We first present a new simpler derivation of the
extended Clausius relation, and clarify its close relation with the linear
response theory. We then derive a new improved extended Clausius relation with
a "nonlinear nonequilibrium" contribution which is written as a correlation
between work and heat. We argue that the "nonlinear nonequilibrium"
contribution is unavoidable, and is determined uniquely once we accept the
(very natural) definition of the excess heat. Moreover it turns out that to
operationally determine the difference in the nonequilibrium entropy to the
second order in the temperature difference, one may only use the previous
Clausius relation without a nonlinear term or must use the new relation,
depending on the operation (i.e., the path in the parameter space). This
peculiar "twist" may be a clue to a better understanding of thermodynamics and
statistical mechanics of NESS.Comment: 31 pages, 4 figure
- …